Exchange Rate Economics: Theories and Evidence

66 Purchasing power parity and the PPP puzzle
Imbs et al. also demonstrate that this kind of bias holds for estimates based on the
aggregate real exchange rate. On the assumption that each sector receives equal
weight in aggregate price index for all countries,the aggregate real exchange rate
is then given by:
q t = 1 N
N∑
q i,t . (2.41)
i=1
In this context the error term from estimating the standard AR1 process,
q t = ρq t−1 + β + ε t ,is given by:
ε t = _
ε it + 1 N
N∑
η i qit−1 T ,(2.42)
i=1
where ¯ε it ≡ 1/N ∑ N
i=1 ε it . Since the error term contains the lagged dependent
variable,through unaccounted heterogeneity,the error term will again be correlated
with the regressor producing inconsistent estimates of the AR1 coefficient
and of the half-life.
Using CPI-based real exchange rates and the sectoral disaggregate components
of these prices collected from Eurostat,over a sample period 1975–96,Imbs et al.
estimate half-lives for the CPI-based real exchange rates of around 4 years,which
is in the usual range,and half-lives for the diaggregate data of between 4 months
and 2 years. They also demonstrate that the degree of heterogeneity is much more
marked for the relative price of traded goods than the relative price of non-traded
to traded goods and,indeed,homogeneity restrictions on the persistence properties
of real exchange rates cannot be rejected. They also demonstrate that the apparent
dominant role of traded goods at long horizons can be traced back to the same
aggregation bias that solves the PPP puzzle.
However,Chen and Engel (2005),using new empirical evidence and theoretical
reasoning,argue that ‘aggregation bias does not explain the PPP puzzle’. They
demonstrate using a simulation analysis that if qt
T is constrained to be nonexplosive
– 1 ≤ˆρ i – then the size of the aggregation bias is much smaller than Imbs et al.
claim. Furthermore,in the presence of measurement error in qt T ,which is additive,
and not very persistent,they show that this can make relative prices appear less
persistent than they actually are. Using the same data set as Imbs et al.,but with
corrections for data entry errors,Chen and Engel show that half-life estimates are
in fact in line with Rogoff’s consensus estimates. Additionally,using two different
bias correction methods they find that the half-life deviations from PPP for this
data set turn out to be even higher than Rogoff’s consensus estimates.
2.4.5 Time aggregation bias
Taylor (2000) argues that the use of low frequency data,such as the annual
data used in nearly all of the panel data sets referred to earlier,does not,by